Problem: The grades on a geometry midterm at Loyola are normally distributed with $\mu = 82$ and $\sigma = 2.0$. Gabriela earned a n $85$ on the exam. Find the z-score for Gabriela's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Gabriela's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{85 - {82}}{{2.0}}} $ ${ z \approx 1.50}$ The z-score is $1.50$. In other words, Gabriela's score was $1.50$ standard deviations above the mean.